Typical bearing lubrication systems for gas turbine engines use heat exchangers to absorb heat from oil that is recirculated through the system once the oil is delivered to bearings included in the gas turbine engine. Heat from the oil is transferred by the heat exchanger to either air passing through the gas turbine engine or fuel injected into the gas turbine engine. Those systems are difficult to integrate into gas turbine engines producing propulsive thrust at supersonic speeds because the temperature of the air passing through the gas turbine engine and the temperature of the fuel injected into the gas turbine engine is often higher than the bearings can withstand in normal operating conditions. In view of the difficulty inherent in recirculating systems, providing a bearing lubrication system for a gas turbine engine producing propulsive thrust at supersonic speeds that does not use recirculated oil remains an area of interest.